Abstract
We consider the generalization of the classical P∥Cmax problem arising when a given limit k is imposed on the number of jobs that can be assigned to any machine. This generalization has practical interest in the optimization of assembly lines for printed circuit boards (PCB). The problem is strongly NP-hard for general k, it is solvable in O(n log n) time for fixed k=2, while it remains strongly NP-hard for any fixed k⩾3. We consider immediate adaptations of simple upper and lower bounds for P∥Cmax, and analyse their worst-case behaviour. We show that the cardinality constraint does not strengthen the LP relaxation of the problem, and that the worst-case performance of the bounds for P∥Cmax generally worsen when they are adapted to the new problem. New specifically tailored lower bounds are introduced, and their average tightness is evaluated through extensive computational experiments on randomly generated test instances. Copyright © 2001 John Wiley & Sons, Ltd.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
